The front wheel of my bicycle was punctured by a small screw nail on the road

I am going to have one day off, so I submit an application form titled like the following:
Application for day off
Application for a day off

You said that your right ankle needed a surgery. Do you need it on a bone or on a ligament?

Do these have the same meaning?
1. I don't need a case and don't need a lanyard
2. I don't need a case and a lanyard
3. I don't need both a case and a lanyard
4. I need neither a case nor a lanyard
5. I don't need either a case or a lanyard
6. I don't need a case or a lanyard    *****